a. To graph the population function P(t) = 3000 / (1 + 200t - 0.4t^2), we need to plot points for various values of t. Let's plot the graph and determine if the population levels off.
b. To estimate when the rabbit population grew most rapidly, we look for the maximum point on the graph. We can find this point by taking the derivative of the population function and setting it equal to zero to find critical points. Then, we evaluate the second derivative to determine if the critical point is a maximum or minimum.
c. Natural causes that could lead to the shape of the graph of P include factors such as limited resources like food and habitat, predation, diseases, and environmental changes. These factors can influence the growth rate of the rabbit population over time.
